document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84753>Question 84753</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The scores for a standardized reading test are found to be normally distributed with a mean of 500 and a standard diviation of 60. If the test is given to 900 students, how many are expected to have scores between 500 and 620? <BR>\n" );
document.write( "A)306<BR>\n" );
document.write( "b) 432<BR>\n" );
document.write( "c)459<BR>\n" );
document.write( "d)612 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61051 by </B><A HREF=/tutors/aboutme.mpl?userid=Scriptor><B>Scriptor(36)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Scriptor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=61051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
document.write( "\n" );
document.write( "Let's calculate the probability that one student has a score between 500 and 600. This is P(500< X < 620)<BR>\n" );
document.write( "I use the notation X for the score:\r<BR>\n" );
document.write( "\n" );
document.write( "P(500 < X < 620) <BR>\n" );
document.write( "= P( 500 - 500 < X - 500 < 620 - 500)  (subtract 500 on all sides)\r<BR>\n" );
document.write( "\n" );
document.write( "= P(0 < X - 500 < 120)\r<BR>\n" );
document.write( "\n" );
document.write( "= P (0/60 < (X-500)/60 < 120/60)       (divide bij 60 on all sides)\r<BR>\n" );
document.write( "\n" );
document.write( "= P(0 < (X-500)/60 < 2)\r<BR>\n" );
document.write( "\n" );
document.write( "Since X is normally distributed with mean 500 and std 60, we have that <BR>\n" );
document.write( "(X-500)/60 is standardnormally distibuted:\r<BR>\n" );
document.write( "\n" );
document.write( "X~N(500,60²) <=> (X-500)/60 ~ N(0,1)\r<BR>\n" );
document.write( "\n" );
document.write( "This means that:\r<BR>\n" );
document.write( "\n" );
document.write( "= P(0 < (X-500)/60 < 2)  = Phi(2) - Phi(0)\r<BR>\n" );
document.write( "\n" );
document.write( "The values of Phi(2) and Phi(0) can be looked up, they are:<BR>\n" );
document.write( "Phi(2)= 0.9772 and Phi(0)= 0.5\r<BR>\n" );
document.write( "\n" );
document.write( "=> P(0 < (X-500)/60 < 2)  = 0.9972 - 0.5 <BR>\n" );
document.write( "                          = 0.4772 <BR>\n" );
document.write( "                          ~ 0.48\r<BR>\n" );
document.write( "\n" );
document.write( "This means that there is 48% that the score will be wetween 500 and 620.<BR>\n" );
document.write( "For 900 students we thus expect that we expect 0.48*900=432 students with a score between 500-620.\r<BR>\n" );
document.write( "\n" );
document.write( "Answer: 432  <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );